Graphing Linear Functions

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x, indicating how steep the line is.

Front

How can you identify the slope from the equation y = mx + b?

Back

In the equation y = mx + b, the slope is represented by the coefficient m.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept is the value of y when x = 0, represented by b in the equation y = mx + b.

Front

How do you find the y-intercept from a linear equation in standard form?

Back

To find the y-intercept from a standard form equation (Ax + By = C), set x = 0 and solve for y.

Front

What is the significance of the graph of a linear function?

Back

The graph of a linear function represents all the solutions to the equation, showing the relationship between x and y.

Front

How do you determine if a graph represents a linear function?

Back

A graph represents a linear function if it forms a straight line.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.